A method to treat a quantum system in interaction with a fermionic reservoir is presented. Its most important feature is that the dynamics of the exchange of particles between the system and the reservoir is explicitly included via an effective interaction term in the Hamiltonian. This feature gives rise to fluctuations in the total number of particles in the system. The system is to be considered in its full structure, whereas the reservoir is described only in an effective way, as a source of particles characterized by a small set of parameters. Possible applications include surfaces, molecular clusters, and defects in solids, in particular in highly correlated electronic materials. Four examples are presented: a tight-binding model for an adsorbate on the surface of a one-dimensional lattice, the Anderson model of a magnetic impurity in a metal, a two-orbital impurity with interorbital hybridization (intermediate-valence center), and a two-orbital impurity with interorbital repulsive interactions.A method to treat a quantum system in interaction with a fermionic reservoir is presented. Its most important feature is that the dynamics of the exchange of particles between the system and the reservoir is explicitly included via an effective interaction term in the Hamiltonian. This feature gives rise to fluctuations in the total number of particles in the system. The system is to be considered in its full structure, whereas the reservoir is described only in an effective way, as a source of particles characterized by a small set of parameters. Possible applications include surfaces, molecular clusters, and defects in solids, in particular in highly correlated electronic materials. Four examples are presented: a tight-binding model for an adsorbate on the surface of a one-dimensional lattice, the Anderson model of a magnetic impurity in a metal, a two-orbital impurity with interorbital hybridization (intermediate-valence center), and a two-orbital impurity with interorbital repulsive interactions.

Physical review. B, Condensed matterJan 15, 199312 citations

Magnetic impurities in spin-1/2 chains

Lara Benfatto

APSMar 1, 20050 citations

Properties of the t 1 − t 2 one-dimensional Hubbard model at finite temperature

SungKun Kim, Hunpyo Lee

The one-dimensional t 1 − t 2 half-filled Hubbard model is considered at finite temperatures T within a dynamical cluster approximation (DCA) with N c = 24 in combination with a semiclassical approximation (SCA) impurity solver. The SCA approach accounts for long-range spatial fluctuations, where exact numerical impurity solvers can not capture due to computational expense, even though dynamical fluctuations are freezing. Therefore, it can consider both frequency- and momentum-resolved physical properties beyond the DCA with small cluster in combination with exact impurity solvers. By the computation of the static spin-spin correlation, the density of states, and the double occupancy, we examine the description of the frustrated one-dimensional systems at finite T within given approximations. We confirm not only the interaction-driven metal-insulator transition in the regions of t 2/t 1 > 0.5, but also the commensurate-incommensurate transition by tunning t 2/t 1 in the strong interaction region. We also observe finite T-driven metal-insulator transition.The one-dimensional t 1 − t 2 half-filled Hubbard model is considered at finite temperatures T within a dynamical cluster approximation (DCA) with N c = 24 in combination with a semiclassical approximation (SCA) impurity solver. The SCA approach accounts for long-range spatial fluctuations, where exact numerical impurity solvers can not capture due to computational expense, even though dynamical fluctuations are freezing. Therefore, it can consider both frequency- and momentum-resolved physical properties beyond the DCA with small cluster in combination with exact impurity solvers. By the computation of the static spin-spin correlation, the density of states, and the double occupancy, we examine the description of the frustrated one-dimensional systems at finite T within given approximations. We confirm not only the interaction-driven metal-insulator transition in the regions of t 2/t 1 > 0.5, but also the commensurate-incommensurate transition by tunning t 2/t 1 in the strong interaction region. We also observe finite T-driven metal-insulator transition.

Journal of the Korean Physical SocietyAug 1, 20170 citations

Quantum Impurity in a Magnetic Environment

Subir Sachdev A

arXiv:cond-mat/0304171Journal of Statistical PhysicsMar 17, 200412 citations

Anderson metal-insulator transitions with classical magnetic impurities

Daniel Jung, Stefan Kettemann, Keith Slevin

We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator transition. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude ${W}_{\mathrm{c}}$ with increasing exchange coupling strength $J$ . The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\ensuremath{\nu}$ and enhances the multifractality parameter ${\ensuremath{\alpha}}_{0}$. The new value of $\ensuremath{\nu}$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator transition. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude ${W}_{\mathrm{c}}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\ensuremath{\nu}$ and enhances the multifractality parameter ${\ensuremath{\alpha}}_{0}$. The new value of $\ensuremath{\nu}$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.

arXiv:1507.03374Physical review. B./Physical review. BApr 5, 20164 citations

{W}_{\mathrm{c}}

with increasing exchange coupling strength

J

. The resulting scaling with

J

is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\ensuremath{\nu}$ and enhances the multifractality parameter ${\ensuremath{\alpha}}_{0}$. The new value of $\ensuremath{\nu}$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.